Sum of Interior Angles of a Polygon

Below are 5 polygons with the measures of their interior angles labeled. In this activity, we are going to investigate and come up with a way to calculate the sum of the interior angles using the number of sides of the polygon.

1) Start with the triangle. What is the sum of the interior angles?
2) Now, move one or more of the vertices. What happens to the sum?
3) Repeat steps 1 and 2 with the other four polygons.
4) What happens to the sum as you add another side? What conclusion can you draw about the sum of the interior angles of a polygon related to the number of sides of the figure?
5) Use your conclusion from question 4 to predict the number of degrees in a decagon and a 27-gon.